Introduction
Geotechnical software,often referred to as modelling software,is now being used routinely in geotechnical practice. In spite of the extensive use,there seems to be some confusion as to what is meant by the word model.Does it refer to a numerical simulation,as in the phrase,‘a finite element model’?Taken in this context,modelling is simply the operation of a numerical tool.This is not only too narrow a definition;it also diverts us from a deeper understanding of modelling as a fundamental engi-neering problem-solving methodology.
In this paper,we explore the defini-tion of the word modelling in some depth.We review the purpose and benefits of modelling to the engineer and introduce a conceptual frame-work that guides us through the mod-elling process.
Modelling Defined
The role of modelling within geotechnical engineering practice was clearly illustrated by Professor John Burland from Imperial College,Lon-don in his1987Nash Lecture,entitled The Teaching of Soil Mechanics–a Per-sonal View(Burland1987).In this lec-ture,he presented the view that geotechnical engineering practice is comprised of three parts:establishing the ground profile,defining ground be-havior,and modelling–all interlinked and supported by experience consisting of empiricism and precedent.He linked
these three parts into what has now be-
come referred to as the Burland Trian-
gle.Morgenstern(2000)also discussed
the Burland Triangle at some length in
his keynote address entitled Common
Ground at the GeoEng2000Conference
in Melbourne,Australia.Graham
(2003),in his Hardy Address at the
Winnipeg Canadian Geotechnical Con-
ference,concentrated on the soil behav-
ior and ground profile apexes of the
Burland Triangle.
The Burland Triangle has been dis-
cussed widely and expanded on consid-
erably since it was first introduced.The
expanded version of the Burland Trian-
gle as presented in the Ground Engi-
neering magazine(Anonymous1999)
is shown in Figure1.Burland envisaged
geotechnical practice as requiring a
clear understanding of the ground pro-
file established from a site investiga-
tion,the definition of soil behavior
provided from field and laboratory
measurements,and then the application
of this understanding through the use of
modelling.It is important to note two
features of this triangle:first,that all
three steps are interlinked and second,
that they are all tied together by
experience.
An important idea in this representa-
tion is how the process of modelling is
integral and integrated into the entire
engineering process.It is the point at
which our understanding of site condi-
tions and soil behavior are developed
44
Geotechnical News, December 2004
Figure 1. Expanded Burland Triangle (Anonymous 1999).into an idealized conceptual model, which can be drawn upon through the use of analytic techniques(numerical models)or physical models to assist us in interpretation and design.The devel-opment of appropriate conceptual and analytic models is interlinked with,and relies heavily on,the information ob-tained from the other parts of the trian-gle.In addition,the development of the models themselves is strongly depend-ent on the experience of the individual engineer and the precedents of the profession as a whole.
In addition to providing perspective on the place of analytic models within geotechnical practice,the Burland Tri-angle also opens our eyes to a broader definition of modelling.As geotechnical engineers,we work with some of the most difficult materials and conditions in any field of engineering. Unlike many engineering professions, we cannot simply specify the types of materials or material geometries with which we would like to work.We live with what nature provides.In fact,de-veloping an understanding of what na-ture has provided is a major portion of the engineering challenge.We deal with an extremely complex physical reality. And yet,to engineer with this reality means we have to try to make some cal-culations.We must turn a complex physical reality into some mathematical system to quantify our designs,and to understand our risk and uncertainty.
The National Research Council
(1990)report on modelling describes
this concept as follows:‘A mathemati-
cal model is a replica of some
real-world object or system.It is an at-
tempt to take our understanding of the
process(conceptual model)and trans-
late it into mathematical terms’.As de-
picted in Figure2,the simplest
definition of modelling is this:the pro-
cess by which we extract from a com-
plex physical reality an appropriate
mathematical reality on which we can
base a design.The role of the numerical
model is simply to assist us in develop-
ing the appropriate mathematical
abstraction.
Modelling Complexity
Modelling,then,is the process by
which we construct a simplified mathe-
matical reality from a more complex
physical reality.In this process we often
make use of numerical methods(or
models)in order to more fully describe
a complex physical reality.A short re-
view of some of these complexities
might help us appreciate the challenge
we face in the modeling process.So
what are some of the complexities we
face in the development of our model-
ling exercise?
In geotechnical engineering,our me-
dium consists of natural geologic mate-
rials that are notoriously variable,both
in terms of their properties and their
spatial distribution.Since soil behavior
is governed by effective stresses,the be-
havior of these geologic materials is in-
trinsically linked to the pore-water
pressures within the soil.Consequently,
we not only have geologic complexity,
we must also deal with complex
hydrogeologic systems.
We also deal with complex behav-
ioural processes.The primary goals of
any geotechnical design are often re-
lated to one of three general types of be-
havior(and properties):deformation
(compressibility),stability(strength),
and seepage or groundwater flow(hy-
draulic conductivity).Each of these
processes can be extremely complex,
and the mathematical descriptions of
this behavior often result in non-linear
numerical solutions.
On top of geologic and behavioral
complexities,we also must work with
complex designs and design methods.
The development of a final design often
requires that we evaluate the perfor-
mance of numerous alternatives in
terms of their constructability,perfor-
mance,and risk of failure.This process
requires that we quantify the perfor-
mance of hundreds,if not thousands,of
different design scenarios.
Finally,we have to communicate
and steer our designs through complex
decision-making processes.This may
appear trivial at first glance,but often
we must find ways of communicating
our designs effectively to decision mak-
ers,including the public.This can often
be facilitated through the use of visual
computer graphics that can be produced
from many of the numerical tools
currently used in analyses.
Homer-Dixon(2001),in his book
entitled The Ingenuity Gap,highlights
how the demand to deal with increasing
levels of complexity continues to accel-
erate in our modern society.This com-
plexity occurs not only due to our
awareness and potential ability to deal
with increasing levels of complexity in
physical processes,but also because of
increasingly higher demands from soci-
ety that these complex interactions be
considered in design.He also points out
that in many cases we are reaching a
limit to the level of complexity with
which we can deal:
Geotechnical News, December 200445
GEOSPEC Figure 2. Simple definition of modelling.“Another way to estimate a system’s complexity is to measure the difficulty of creating a mathematical model of it.…. Some systems are extremely difficult to model because they have so many com-ponents;to use the specialists’awkward phrase;they are“mathematically in-tractable”.As the number of compo-nents,variables,or“dimensions”in the equations goes up,the length of time it takes to work out,or solve,the equa-tions rises even faster.…Although mod-ern supercomputers can help solve this problem,even the fastest computers are often quickly overwhelmed.As top ex-perts,Joseph Traub and Henryk Wozniakowski,say,…Even though sci-entists have computers at their dis-posal,problems can have so many variables that no future computer speed will make it possible to solve them in a reasonable amount of time”(Homer-Dixon 2001 p. 116).
In an attempt to deal with this com-plexity,we continue to extend the com-plexities of our modelling tools.This rapid expansion in the use of increas-ingly complex modelling tools is oc-curring not only in engineering,but also in financial markets,global warm-ing,and the management of social pro-grams.Homer-Dixon points out that, while these computer tools are increas-ingly being used by young,computer literate professionals,they are often too intimidating for older,experienced professionals.This results in a situa-tion where the people running the mod-els do not have the professional experience or wisdom to use the tools effectively.He writes:
”Says Gene Rochlin,a professor of energy and resources at the University of California,Berkeley;‘As skill with the computer and its models becomes more important than accumulated ex-perience,power and influence are shift-ing to a generation of younger traders more familiar with electronics than trends,less concerned with preserving long-term market stability than with de-veloping and mastering better,quicker models with which to outmaneuver the competition..…We are now acutely aware how(in many fields)more expe-rienced managers are actually intimi-dated by a younger generation steeped in the arcane of computers and their
magical,number-crunching software.
Experiential knowledge consists of in-
tuitions,subtle understandings,and
finely honed reflexes gained through
years of intimate interaction with a
given natural,social or technological
system.…When we fragment manage-
ment expertise into subspecialties and
squeeze out broad experiential knowl-
edge,we become more vulnerable to
unknown unknowns”(Homer-Dixon,
2001, p. 177-178).
Although his quote is written in the
context of the near failure of the stock
markets during the October19and20,
1987crises,it sounds all too familiar to
our own engineering practice.In the
next section,we discuss how to include
both the computer hotshot and the sage
in the modelling process.
Application of Models
Recognizing that we use numerical
tools to deal with complexity,the next
questions we address are ones of expec-
tation.How do we use these models?
What is the primary strength of the
modelling process in general,and the
application of numerical tools such as
computer models in particular?
One could classify the use of models
in many ways,but we suggest three ge-
neric categories:
•Interpretation:This is the use of
models to help us interpret field or
laboratory data.For example,the de-
velopment of a model to help
back-analyze a suite of monitoring
information.
•Design:In this application,we de-
velop models to help compare the
relative performance of various de-
sign alternatives,with less emphasis
on the final predicted performance.
•Prediction:Finally,we may have to
use a model to provide a final,quan-
tifiable prediction of actual field be-
havior.
It would be interesting to ask a group
of engineers to assign percentages to
each of these applications in terms of
the effort they expend in each type of
exercise.The response could be com-
pared to a survey of the general public
as to how they perceive engineers make
use of models.Although we can only
speculate on the actual numbers,we
suspect that most engineers would al-
locate the majority of model applica-
tion to the categories of Interpretation
and Design–let’s say90to95%be-
tween the two.Most of us would be
very uncomfortable with assigning
more than5or10%of the modelling
effort to prediction.However,one
might suspect that the general public
would see most of what we are trying to
do as prediction.
This is a significant point because,
if we don’t believe we can predict,
then why would we engage in the
modelling process at all?Let us ad-
dress this issue directly.How well do
you believe we can make predictions
in geotechnical engineering?In many
of our estimates(note the softening of
the word),we would be happy to be
within an order of magnitude.We
would be extremely pleased if we had
predicted10cm of settlement behind
a retaining structure only to actually
measure1cm.(We would likely not
be quite as happy if the situation was
reversed but we suspect we would still
be satisfied with our estimate.).
Maybe we can’t really predict at all!
If that is the case,then why do we go to
all this bother?Let’s look at an example
of how well we predict.Carter et al.
(2000)presented an example from the
German Society of Geotechnics in his
Keynote address at GeoEng2000in
which a number of different groups had
been asked to predict the deflection of a
tie-back retaining wall.The groups
were all given the same site information
(e.g.ground profile and ground behav-
ior).The results of the various predic-
tions are shown in Figure3along with
the actual monitoring data.The dashed
dark heavy line is the actual inclinome-
ter data.The solid dark heavy line is the
inclinometer data shifted to the left to
account for an estimated base
correction.
There may be a few readers who will
be quite concerned about the lack of
agreement between the predictions and
the monitored reality and possibly even
more so about the lack of agreement be-
tween the various predictions.In fact,
the accurate prediction of actual field
performance is extremely difficult.We
GEOSPEC
46Geotechnical News, December 2004
may try to predict the amount of settle-ment or seepage,the first arrival of a contaminant,or the stability of a slope;however,the accuracy of those predic-tions are often overwhelmed by diffi-culties in fully characterizing the geologic setting (in three dimensions),in providing appropriate theoretical de-scriptions of soil behavior,in uncertain-ties in measuring soil properties,and in numerical problems with analytic tools.Because of these difficulties,model-ling,and particularly the use of numeri-cal models,is often dismissed as useless due to lack of predictive accuracy.In fact,we would contend that we can take a lot of encouragement from the predictions shown above.In nearly every case,the general pattern of move-ment was correctly predicted and the magnitude of the movement was well within an order of magnitude.The pre-dictions were all wrong,and yet they provided considerable insight into the performance of this structure.More-over,the predictions provide sufficient insight so that the structure could have been designed safely and economically.This is a critical les-son in modelling and
the use of numerical models in particular.We previously as-cribed the majority of
engineering use of
computer models to the categories of inter-pretation and design,not prediction.It is an important distinction because we believe that the key advantage
of modelling,and in
particular the use of computer modelling
tools,is the capability it has to enhance engi-neering judgment ,and not the ability to en-hance our predictive
capabilities.Although
the use of more sophis-ticated computer tools
does allow us great ad-vantages in prediction over other methods
such as hand calculations,graphical
techniques,and analytic solutions,this is secondary to the capability of models to enhance engineering judgment.
The reason for this is because model-ling is primarily about a process,not about prediction.Anderson and Woessner (1992)provide this insight:
“The attraction of...modelling is that it
combines the subtlety of human judg-ment with the power of the digital com-puter .”The primary role of the modelling process as described by
Burland and others,which is the one we espouse in this paper,is that it is a pro-cess .When this process is entered into correctly,it incorporates and enhances the essential component of engineering design that cannot be replaced by a
computer:experience and judgment.There is no question that the com-plex numerical tools we have today do provide us much better predictive capa-bility than we have ever had before.And yet,this is not the primary benefit we
have from the modelling process.The modelling process is most powerful
when it is used as an aid to our own
judgment.As we will see later,it also al-lows us immense freedom.It allows the freedom to model even when we can only guess at geology and material properties,and the freedom to recon-nect the wise,old,seasoned profes-sional with the young computer guru.In the end,modelling,done correctly,helps ensure that we have not only ex-tracted an appropriate level of complex-ity from the physical reality in our mathematical model,it teaches us and helps us develop a sound understanding of the physical system so that we can,and as we inevitably must,exercise our engineering judgment.
Taken in this light,we can see how we receive the maximum benefit from modelling when it incorporates and is applied to the entire process of data gathering,interpretation,design and fi-nal prediction.The modelling process must envelop site investigation (ground profile),field and laboratory testing and monitoring (ground behavior),as well as theoretical idealization and numeri-cal analyses.Let us now move on to look at a possible model for this model-ling process.In the next section we de-velop a series of generic steps to describe this process,outlining the activities,challenges and pitfalls facing us in each step.
A General Methodology for Modelling
There are relatively few references in literature that describe a model for mod-elling.Some references are provided at the back of this paper if you would like to read further in this area.A typical ex-ample of a modelling methodology would be one proposed by Mercer and Faust (1981)for groundwater model-ling.They suggest the following steps:•Develop an understanding of the physical system (Conceptual Model)•Translate physics describing your understanding into a mathematical system (Mathematical Model)
•Develop a solution of the mathemati-cal model using numerical,analytic,graphical,analogue or other tech-niques (Numerical Model)
Some other references could be cited here,but like the example of Mercer and
Geotechnical News, December 2004
47
GEOSPEC
-60-50-40-30-20-10010
04
812
16
2024
28
32Depth below surface (m)
Deflection (mm)
-60-50-40-30-20-1001
measured
computed
Figure 3. Predicted and measured deflections of a tie-back wall (Carter et al. 2000).
•Conceptualize:Geology and the physical processes
•Define:Behavioral processes and material properties •Formulate:Numerical descriptions and solutions for these processes •Solve:Obtain an accurate numerical solution
•Interpret:Validate,calibrate and in-terpret the solutions in the context of the physical system
We could also develop a modelling process along the lines of an engineer-ing design process.A colleague at the University of Saskatchewan,Professor Jerry Huff,describes the design process to undergraduate students as being comprised of combinations of the fol-lowing four words:generally,specifi-cally,what,and how.These words are combined into four questions,to be ad-dressed in order,to move us towards a final design.
•Generally–What?This is a state-ment of work.What,in general,are we trying to build?What general ob-jectives do we have?What is the gen-eral characterization of the physical environment(e.g.geology)in which we must work?•Specifically–What?What are the specifications for performance?
What are key processes and proper-ties with which we must work?What are the quantitative inputs and out-puts we will need?•Generally–How?What analytic tools can we use to quantify behav-ior?To which input parameters are the behaviours of interest sensitive?
What is the relative performance of various design alternatives?•Specifically–How?What will be the final recommended design?
What are the final predictions and what aspects of the design are essen-tial to the accuracy of these predic-tions?
Another approach to this process is to look at it in terms of a simple version of the scientific method:observe,mea-sure,explain,and verify.These are most commonly defined as part of the scientific method as follows:•Observe–Definition of the problem
statement based on general observa-
tions
•Measure–Collection of problem
specific data
•Explain–Development of a hypoth-
esis explaining the behavior
•Verify–Validation of the hypothesis
by comparing the explanation to the
data
When adapted to the modelling pro-
cess,these four steps become:
•Step1:Observe–Develop a concep-
tual model of the ground profile and
the project objectives
•Step2:Measure–Define appropri-
ate theoretical models that describe
the key processes operative in the
problem.
•Step3:Explain–Develop a mathe-
matical description of these pro-
cesses and verify that it provides an
accurate solution.
•Step4:Verify–Interpret the results
of the mathematical description in
light of the observed physical reality.
Prove the hypothesis,obtain addi-
tional measurements,improve the
complexity or accuracy of the math-
ematical solution,or change your
conceptual understanding until you
are satisfied that you have a full un-
derstanding of the physical reality.
Each of these steps are discussed in
more detail in the following section in-
cluding a description of typical activi-
ties conducted during each phase of the
modelling process along with warnings
about potential pitfalls.The reader is
also directed towards a useful illustra-
tive example of this process provided in
the National Research Council(1990)
booklet entitled Groundwater Models:
Scientific and Regulatory Applications.
Step 1:Observe–Develop the
Conceptual Model
There are three key activities for this
step of the modelling process.First,it is
important to clearly define the purpose
of the model.What are the‘generally–
what?’questions you are concerned
about?
The second activity is to begin to
gather existing general information for
your site.In some cases,you will only
have access to existing background in-
formation from geologic maps or re-
ports.In other cases,there may have
been some preliminary site investiga-
tion.It is essential at this stage to begin
to develop a conceptual model of the ge-
ology and hydrogeology of the site.In
the case of new construction,you will
also need information on the proposed
development such as potential depths of
excavation,loadings,sequence of
construction and so on.
Finally and most importantly,you
must use your engineering experience
to begin to develop a conceptual model
of the physical environment.Examine
and interpret the existing data into some
sort of coherent conceptual model.
Keep in mind that this model is likely to
evolve repeatedly over the course of the
modelling process as it is challenged by
new data,simulation results and moni-
toring information.However,you must
begin with a commitment to some ini-
tial conceptual model.Being wrong at
this stage is not a problem;being lost or
noncommittal is a problem.The central
component of this conceptual model is
your understanding of the geologic and
hydrogeologic framework of the site.
It is essential that Step1be under-
taken carefully since it serves as a foun-
dation for Steps2,3and4.Major errors
at this point can hopefully be overcome
as we iterate through the four steps;
however,the old adage,‘garbage in=
garbage out’is quite appropriate at this
stage.A somewhat simplistic initial
conceptual model based on existing
data is not fatal;misinterpretation of the
data entirely may be.
It is also important to start simple.
Keep in mind that the modelling pro-
cess is iterative.Increasing the com-
plexity of the initial conceptual model
may be required as the model evolves;
however,speculating on high degrees
of complexity in the absence of sup-
porting field observations is not only
problematic in developing a clear un-
derstanding of site behavior,it will also
make the remaining processes more
difficult.Don’t use too complex a con-
ceptual model too soon.
We think it is obvious that it is impor-
tant to have the sage professional fully
involved in this initial step.The com-
puter skill of the young engineer is no
GEOSPEC
48Geotechnical News, December 2004match for battle scars at this modelling step.We would encourage a young en-gineer faced with a modelling task to seek out the sage in your company to guide you at this stage.
Step 2:Measure–Define the Theoretical Model
An appropriate theoretical description of the important processes must now be selected based on the problem defini-tion and conceptualization provided in Step1.The key material behaviors that will need to be understood must be identified and likely some homework will have to be undertaken to ensure that the theory describing these processes is fully understood.
Each of the constitutive relation-ships describing these processes will have material properties associated with them.The solution will require that we utilize these theoretical descrip-tions to develop governing equations that can be solved,subject to appropri-ate material properties and boundary conditions.Most of these formulations are based on key assumptions,the rami-fications of which need to be appreci-ated in light of our specific problem.
We can also begin to develop an ap-propriate data set that we can use in so-lution.Initially,these might simply be guesses.Often we are reluctant to guess;but keep in mind,the goal of this modelling exercise is to enter into a pro-cess in which we can improve our judg-ment and understanding of the response of the system,it is not to be simply pre-dictive.Professors John Burland and John Carter both advocated the idea of starting with a guess in their keynote ad-dresses at GeoEng2000in Melbourne. Professor Burland notes that this is where they began as they tried to solve the important problem of correcting the increasing lean of the Tower of Pisa.
We may rely solely on reasonable guesses of material properties and boundary conditions during our first pass through this iterative process.The results of our analyses and interpreta-tion will guide us towards understand-ing which parameters are of greatest concern and in which areas our greatest uncertainties lie.Additional field work or laboratory testing can then be di-rected towards to resolving some of the
most important uncertainties,and our
mathematical descriptions of the
physical reality can then be improved.
It is important also to realize that ex-
isting field monitoring can be an impor-
tant source of information to describe
material behavior.We can begin with a
guess,but then use actual monitored
field responses in space and time along
with the completion of Steps3and4to
back-analyze guesstimates of
appropriate material properties.
The most common sources of error
in this step are primarily related to theo-
retical awe:our tendency to accept
without question the theory incorpo-
rated in the most readily accessible
mathematical solution or numerical
model.It is important to do your home-
work at this step.Make sure that you are
comfortable with the fundamental the-
ory being used in the mathematical de-
scription of your system.We are not
sure whether the sage or novice engi-
neer has a greater advantage here.The
sage has had years of practice but faces
the challenge of staying current with the
latest theoretical developments,while
the novice has had the most recent for-
mal education,but is now regretting
they didn’t pay more attention in class.
In either case,the only solution is to re-
turn to the books and study.
Step 3:Explain–Develop and
Verify the Analytic or
Numerical Model
Now that the physical reality has been
observed and conceptualized,and the
relevant processes have been theoreti-
cally and mathematically defined,it is
now time to test these descriptions by
committing them to a mathematical
solution.
In many cases,the solution takes the
form of a boundary value problem.This
type of mathematical problem is de-
fined by the following components.
First a domain(geometry)must be de-
fined within which we will seek the so-
lution to a set of governing equations.
These equations will be solved subject
to a set of boundary conditions applied
to the domain and in concert with a set
of material properties specified within
the domain.The method of solution can
be quite varied,encompassing analytic
solutions,graphical techniques(e.g.
flownets)or numerical solutions such
as finite difference and finite element
techniques.
An appropriate method of solution
for the equations laid out in Step2is se-
lected.In most cases,it is important to
select more than one method of solu-
tion,such as an analytic solution and a
numerical solution.The complexity of
the model may eventually require the
use of a numerical model such as a com-
mercial software package;however,it is
important that even these models be
verified against other solutions.This
might require that a simpler conceptual-
ization be used initially or that simpler
versions of similar problems be com-
pared.The purpose of this exercise is
twofold.It verifies that the more com-
plicated numerical model used by the
engineer is working correctly,and it
also familiarizes the user with the par-
ticular features and peculiarities of the
software(input and output)to ensure
they are using the software correctly.
If this is the first time you are using
this particular method of solution,then
we would encourage you to check the
method against known analytic solu-
tions,other known numerical solutions
and even other case histories of field
studies from literature or your own files.
The goal here is not simply to get a
solution to your particular modelling
problem.It is to develop confidence in
the limits of the solution.This is of par-
ticular concern with numerical models
where numerical problems of roundoff,
convergence,spatial and temporal
discretization,numerical oscillation,or
dispersion,may occur.These errors are
not always as easy to identify as the
limitations of an analytic solution.
A useful metaphor might be to com-
pare the engineer with a numerical solu-
tion to that of an artisan or workman
with his tools.You must have confi-
dence with the tool in order to work
freely and confidently on the project.
Step 4:Verify–Interpret,
Calibrate, Validate against the
Physical Reality
Once a mathematical solution is ob-
tained,the results must be carefully in-
Geotechnical News, December 200449
GEOSPEC
terpreted and checked against the physi-cal reality.Typical exercises might include a comparison against field mon-itoring in which the conceptual and mathematical models are adjusted until there is good agreement between the physical and mathematical systems.It is important to realize that these calibra-tions are always non-unique.We can improve our confidence in the calibra-tion if we have a series of readings that are taken at different locations and at different times,including both pre-con-struction and during construction. However,keep in mind that we are like the young student trying to solve for four unknowns with three equations. There is no unique solution and any so-lution we can obtain will rely heavily on experience and engineering judgment.
We can also conduct sensitivity anal-yses as an aid to our interpretation.This is a series of simulations in which we vary only one parameter at a time and then review the effect of these variations against key performance(e.g.pore-wa-ter pressure at particular locations,fac-tor of safety,deformation along a retaining structure,etc.).The goal of the sensitivity study is to help us under-stand which element of the conceptual and theoretical models(e.g.boundary condition,material property)are of particular importance to field performance.
It is important at this stage to retain one of the key personality traits of all good engineers:skepticism.All solu-tions should be only considered to be conditionally valid.That is,they are only as good as our conceptual model, mathematical description,and numeri-cal solution.Consequently,it is impor-tant that the sage and the novice be working in concert at this point.
The greatest danger at this stage is blind acceptance of the solution,a prob-lem that is often associated with the use of commercial software.It is important to keep in mind that the solution pro-vided by the software is only one step in the modelling process.It is not design software,only analytical software.The design only comes from the clear think-ing and judgment of the engineer.
This leads to the Golden Rule of the modelling process.Consider suspect any model results that contradict sound
engineering intuition.The basic ques-
tion remains,‘are the results reason-
able?’In the early stages of the
modelling process it is not uncommon
to see results that don’t make sense.Of-
ten it is because of errors in one of the
previous stages of the process:poor
conceptualization,inappropriate mate-
rial descriptions,or even mistakes in
running the numerical software.How-
ever it may also be due to the fact that it
takes some time to train our own think-
ing as to why the predicted behavior is
reasonable.Remember,one of our ob-
jectives is to train our own thinking and
improve our judgment.
Key Points
There are a number of features of nu-
merical models that must be appreci-
ated to make effective use of these ana-
lytic tools in the modelling process.
These features include the fact that all
models are only simplified abstractions
of a complex reality.It is important to
keep in mind that the purpose of model-
ling,particularly in the use of numerical
models,is not to try to replicate all of
nature’s complexity.The genius in
modelling is the ability to only develop
as complicated a representation of the
physical reality as required to suffi-
ciently understand the behavior re-
quired for a particular design.
Understanding this simple concept
helps the engineer appreciate why the
modelling process always begins with
the simplest possible conceptual model,
and then adds complexity incrementally
until the level of complexity is sufficient
to represent the material behavior of in-
terest.This is very much in keeping
with Occam’s Razor,often called the
principle of parsimony,ascribed to the
English philosopher William of Occam
(or Ockham)(1285-1347/49),which
states‘plurality should not be assumed
without necessity’or more simply
stated:‘When there a number of possi-
ble explanations for a phenomenon,
generally,the simplest explanation is
the best’.
Ironically,the basic reason we use
complicated numerical models is so that
we can sort through the complexity of
the physical system until we isolate one
or two simple issues on which we can
base our design.Inevitably,as you be-
gin to reach the end of a long and
lengthy modelling project,you will find
that your understanding of what ap-
peared to be a complex enigma will sud-
denly boil down to one or two central,
simple ideas.In many cases,there is al-
most a sense of personal embarrass-
ment that you didn’t grasp these simple
principles from the beginning.
This is a critical lesson in modelling
and the use of numerical models in par-
ticular.The key advantage of
modelling,and in particular the use of
computer modelling tools,is the capa-
bility it has to enhance engineering
judgment,not the ability to enhance our
predictive capabilities.While it is true
that sophisticated computer tools
greatly elevate our predictive capabili-
ties relative to hand calculations,graph-
ical techniques,and closed-form
analytical solutions,prediction is not
the most important advantage these
modern tools provide.As noted earlier,
numerical modelling is primarily about
process,not about prediction.
Keep it Simple
The first lesson is this:start simple and
then add complexity in increments.This
applies to all steps of the modelling pro-
cess.Begin with the simplest geologic
and hydrogeologic conceptual model
that is consistent with the available data.
Start with a simple theoretical model.
For example,never initiate a non-linear
elastic-plastic stress deformation model
until you have fully explored the impli-
cations of simple linear elastic behav-
ior.Begin with the fewest elements and
least number of materials possible in
your first finite element solution.Add
more elements and materials only as
you understand the behavior of your
simpler system and only until adding
additional elements or materials contin-
ues to make a difference to the behavior
of the system.
A supplementary principle to start-
ing simply and increasing complexity
incrementally is to keep in mind that all
models are data deficient.If you don’t
believe that,then ask any geotechnical
engineer whether they wouldn’t like an-
other one or two boreholes for their pro-
GEOSPEC
50Geotechnical News, December 2004ject.What this means is that we are always working with under-constrained systems with more unknowns than equations.Sherlock Holmes,the great detective(modeller)once said:“It is a capital mistake to theorize before one has data.Insensibly one begins to twist the facts to suit the theories,instead of theories to suit facts”.Dealing with data deficiency means that we must never in-crease the complexity of our theories beyond the level of our data sufficiency and secondly,we have no possible solution without the liberal use of engineering judgment.
There are also a number of practical advantages to starting simply and add-ing complexity incrementally.First,it is much easier to spot errors in your nu-merical model when you begin simply. Errors in specifying material properties or in mesh creation can be seen more readily.One of the first tasks a modeller faces once they have completed their first set of simulations is to verify that what they thought they specified as in-put was actually used.This is much eas-ier to do when the initial complexities are minimized.When you start with a very simple model you are often able to make initial checks on your results with simple hand calculations or analytic so-lutions.
The second advantage of beginning simply is that you are able,in a sense,to begin running sensitivity analyses.You begin to develop an intuitive feel as to when the system begins to change quite dramatically to changes in level of discretization,or the location of a par-ticular boundary condition,or the addi-tion of a different soil property.You lose this intuition when you simply dump all your complicating factors into your simulations at the same time. Questions and Answers
To reinforce the central ideas behind the modelling process,let us consider some complaints or questions a young engi-neer might have as they begin the mod-elling process.
Observe
•Problem:“I really don’t understand the geologic or hydrogeologic sys-tem”.•Answer:Find a sage,talk to senior
staff.At one of our workshops,we
spoke with a consultant who de-
signed their offices so that pairs of
junior and senior engineers sat at
desks across from each other.Con-
ceptualization requires experience:
find an old engineer!
Measure
•Problem:“I don’t think we really un-
derstand this process”.
•Answer:Do your homework.Study,
read,take a class,and/or attend a
workshop.
•Problem:“I don’t have very much
real data”.
•Answer:Start with a guess and then
do sensitivity analyses to see which
parameters are important.
Explain
•Problem:“How do we know if we
have enough time steps or elements
for example?
•Answer:Change it.If it makes a dif-
ference,then it was important.
•Problem:“Is my boundary condition
far enough away?”
•Answer:Change it.If it isn’t a real
boundary condition(symmetry or
geologic control)then simply move
it farther away.Keep moving it back
until it has no further incremental ef-
fect on the solution.
•Problem:“Should my constitutive
model be linear,non-linear,or cou-
pled?”
•Answer:Change it.Start with a sim-
ple enough model so that you are
able to understand the results,and
then change it in small increments of
complexity.
Verify
•Advice:Verify, verify, verify……
•Verify your input data.Did you get
the result you thought you assigned
for material properties,boundary
conditions, etc.?
•Verify your output.Did you get a re-
sult that you expected?Is it reason-
able?Can you approximate the same
result with a hand calculation or sim-
pler analytic solution?Does it agree
with other numerical solutions?
•Advice on calibration:When you
compare your simulation to the re-
sults of monitoring(pore-water
pressures,deflections,etc.),don’t
just compare the specific numbers,
compare patterns.If the numbers
are similar but the pattern(spatial
and temporal variation)is com-
pletely wrong,then you likely have
something wrong with your model.
If the numbers are different but the
patterns are similar,then you likely
have the process sorted out,al-
though your parameters may be off.
(Although getting an exact match
can be a case of diminishing returns.
There is an Irish saying:‘The devil
is in the details’.)In the case of cali-
bration the pattern,not the number,
is the detail.
How Not to Model
Just in case the above advice falls on
deaf ears,let us try some reverse psy-
chology.Here is an example of how
NOT to model effectively:Create a
HUGE mesh and include the highest de-
gree of complexity you can.Dump all
your information into the model and
hope that somehow the software will
magically sort everything out.In short,
the hope is that software will do your
thinking for you.This simply will not
happen!
Concluding Remarks
Our hope is that these informal com-
ments will provide some perspective,
particularly to younger engineers,as
they begin to use the vast power of nu-
merical tools.Keep in mind that the
ability to model effectively is an ac-
quired skill.It is an art,not just a sci-
ence,and like any art form the only
way to learn is to practice.Remember
that modelling takes time,time to
think,time to try and experiment.
There is no such thing as running a
‘quick model’.That is an oxymoron,
like‘good grief’or‘designer jeans’.If
you ask anyone with a considerable
amount of modelling experience,they
will assure you that any modelling ex-
ercise is likely to involve hundreds,if
not thousands,of simulations.It is of-
ten difficult to keep track of all of
these trials(and errors),so we would
encourage you too keep a journal of
Geotechnical News, December 200451
GEOSPECyour thinking and simulation trials.
In the end,the answer to the question posed in the title is that modelling is more about process than prediction. The modelling process is indeed a jour-ney of discovery-a way of learning something new about the complex be-havior of our physical world. Furthermore,it is a process that can help us more fully understand highly com-plex real physical processes,and that can help us exercise our engineering judgment with increased confidence to make predictions. Acknowledgements
The authors would like to acknowledge the patience of innumerable students and workshop attendees who have lis-tened to numerous‘stimulating lec-tures’(another oxymoron)on this topic during graduate classes and workshop training sessions.
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GEOSPEC
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